Head teachers are warning of "volatility" in this year's A-level results and that some lowered grades seem to be "unfair and unfathomable".
In England, 36% of entries had a lower grade than teachers predicted and 3% were down two grades, in results for exams cancelled by the pandemic.
But the overall results, across England, Northern Ireland and Wales, show record highs for A* and A grades.
Controversy has surrounded how results have been decided.
There was "deep frustration" in schools about the confusion caused by late changes to the results system, including the use of mock grades, said Geoff Barton, leader of the ASCL head teachers' union.
"While there has been an overall increase in top grades, we are very concerned that this disguises a great deal of volatility among the results at school and student level," said Mr Barton.
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"We have received heartbreaking feedback from school leaders about grades being pulled down in a way that they feel to be utterly unfair and unfathomable. They are extremely concerned about the detrimental impact on their students."
For the top A* and A grades, independent schools in England saw the greatest improvement on last year - up 4.7 percentage points.
This compares to a 1.7, 2 and 0.3 percentage points improvement for top grades for England's academies, comprehensives and colleges respectively.
The Sixth Form Colleges Association has called the system for calculating A-level grades, "flawed and unreliable" after almost all colleges said grades were lower or much lower than predicted.
A third of college principals also reported results lower or "dramatically lower" than their historic exam performance.
But the Education Secretary Gavin Williamson said the "majority of young people will have received a calculated grade today that enables them to progress to the destination they deserve, with the added safety net of being able to appeal on the basis of their mock results, as well as the chance of sitting autumn exams".
He also said it was "incredibly important" that the moderation process for results did not unfairly disadvantage deprived youngsters or black and ethnic minority communities.
The exam results show:
for A-levels: 9% of entries were A* (up from 7.8% in 2019) 27.9% were A* and A (up from 25.5% in 2019) these are the highest ever levels of A* and As - up from a previous high of 27% in 2011 78.4% of entries were A*-C (up from 75.8% in 2019) Psychology now the second most popular subject, after maths girls outperform boys, except in A*s in England, the moderation means that 36% of results have been lowered by one grade, 3% by two grades, 2% have increased there will be 25,000 university courses available in clearing, including 4,500 in top Russell Group universities for vocational qualifications, the Department for Education says results "broadly in line with previous years"The proportion of entries getting an A* or A grade is at a record high this year - with the 27.9% above the previous highest of 27% in 2011.
Image copyright PA Image caption Brenda Irabor from Ark Academy in Brixton, south London, achieved three A* gradesAnd there are increases in those getting A* to C - as the exam regulator had promised a more lenient approach.
Students taking vocational exams have been getting estimated results over recent weeks - with 250,000 getting BTec results this year - and the Department for Education says vocational results are "broadly in line with previous years".
Heads teachers warn of appeals
At Wilberforce Sixth Form College in Hull, while some students were celebrating, others were very disappointed.
Head teacher Colin Peaks said he had never seen "such a negative feeling" on results day in all his years of teaching.
Mr Peaks said there was "something worrying across the board", with many good students not getting the grades they would have expected.
"The anomalies within the system aren't right - I'm seeing anomalies across the piece that do not make sense to me."
He said basing results, in part, on last year's students' results was wrong because "they're different".
"We are going to see lots of appeals," he added.
Almost 300,000 teenagers received their A-level results - some by email and others going into school, perhaps for the first time since they left in the lockdown in March.
The moderation process means almost 40% of results are lower than the grades submitted by schools - and 2% are higher.
Image copyright Reuters Image caption Students at Crossley Heath Grammar School in Halifax receive their resultsIn England, the key pieces of evidence for deciding grades has been the ranking order of pupils and how schools performed in previous years.
There will be scrutiny of whether this process has particularly disadvantaged poorer students - a problem that caused protests and a U-turn in Scotland.
For students hoping for university places, it is expected to be a "buyer's market", with the admissions service Ucas saying universities would be "super flexible", even for those who have missed grades.
Image copyright PA Media Image caption In Scotland, protests prompted a change in how grades were calculatedIn England, head teachers angrily complained of a "shambles" at the last-minute switch to a "triple lock" in which students could get whatever was highest out of three assessments:
their estimated grade an optional written paper in the autumn or an appeal through their school if the estimated result is lower than the mock examHeads warned mock exams were run in many different ways by schools and it was wrong to try to use them to decide exam results.
England's Education Secretary Gavin Williamson told BBC Breakfast he will refuse to follow Scotland's lead in allowing students whose results were downgraded to be awarded the grades predicted by their teachers.
Image copyright ReutersHe said that would be "unfair to so many students", including the classes of 2019 and 2021.
He admitted there would be some students getting grades "that aren't reflective of the work they've put in" but there would be a "robust appeals process".
He congratulated students on "getting through this extraordinary year", adding that the class of 2020 would not "lose out because of Covid-19".
Labour leader Sir Keir Starmer said: "Something has obviously gone horribly wrong with this year's exam results.
"Nearly 40% of young people have had their grades marked down and that's thousands of young people whose opportunities could have been dashed."
Wales education minister Kirsty Williams said she had to act after other nations had changed from the system of standardisation to ensure Welsh students were on a level footing.
Image copyright PA Media Image caption Twins Rosy (left) and Teddy Valentine received their results at Norwich School on ThursdayThe exam boards have said the results do not show widening gaps or "unconscious bias", such as towards ethnic minority students.
But the linking of students' grades to the results of their schools in previous years will mean close attention to whether this works against disadvantaged children.
This emerged when exam results were published in Scotland - forcing a switch to using teachers' predictions.
And in England there will be concerns that bright pupils in under-performing schools could be marked down.
England's exam watchdog has said that if teachers' predictions had been used it would have inflated results - so that about 38% of entries would have been A* or A grades.
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